Internal combustion engines discharge exhaust gas containing components such as hydrocarbons (HC), carbon monoxide (CO), and nitrogen oxides (NOx). Three-way catalysts are used to purify such components. The purification performance of such three-way catalysts are higher when the air-fuel ratio of the exhaust gas (hereinafter referred to as “exhaust air-fuel ratio”) is maintained approximately at the stoichiometric air-fuel ratio. Thus, to purify exhaust gas using a three-way catalyst, it is necessary to control the amount of fuel to be supplied to the combustion chamber and other parameter, so as to bring the exhaust air-fuel ratio to approximately the stoichiometric air-fuel ratio.
For this purpose, most internal combustion engines are provided with an air-fuel ratio sensor disposed in an engine exhaust passage and upstream of the three-way catalyst to detect the exhaust air-fuel ratio. The amount of fuel to be supplied to the combustion chamber is controlled so as to bring the exhaust air-fuel ratio detected by the air-fuel ratio sensor to approximately the stoichiometric air-fuel ratio by feedback (F/B) control (hereinafter referred to as “main F/B control”).
Disposed upstream of the three-way catalyst, however, the air-fuel ratio sensor may produce unstable outputs due to nonuniform exhaust gas, or may be deteriorated by the heat of the exhaust gas. Thus, the air-fuel ratio sensor may be unable to accurately detect the actual air-fuel ratio. In such a case, the control precision of the air-fuel ratio by the main F/B control described above is lowered.
With this in view, so-called “double sensor systems” have already been in practical use. The double sensor systems are provided with an additional air-fuel ratio sensor disposed also in the engine exhaust gas passage but downstream of the three-way catalyst to detect the exhaust air-fuel ratio. The double sensor systems can improve the control precision of the air-fuel ratio sensor by performing sub-F/B control, which corrects an output value of the upstream air-fuel ratio sensor (and consequently the fuel supply amount) based on an output of the downstream air-fuel ratio sensor such that the output value of the upstream air-fuel ratio sensor coincides with the actual air-fuel ratio.
At cold startup of an internal combustion engine, for example, startup fuel amount increase control is performed in which the fuel supply amount is increased compared to that when the internal combustion engine is in normal operation, in order to stabilize the combustion of an air-fuel mixture in a combustion chamber. During the startup fuel amount increase control, the fuel supply amount is adjusted and the air-fuel ratio is subjected to open control. After the startup fuel amount increase control is finished, F/B control is performed.
In this case, however, the F/B control is not started until the startup fuel amount increase control is finished, which requires a longer time since the startup of the internal combustion engine until the start of the F/B control. The exhaust air-fuel ratio often does not achieve the target air-fuel ratio before the start of the F/B control, which adversely affects the exhaust emission. Therefore, it is required that the F/B control is started immediately after the cold startup of the internal combustion engine.
JP-A-2003-3891 discloses an air-fuel ratio control system that starts F/B control so as to bring the actual exhaust air-fuel ratio to the target air-fuel ratio and reduces the proportion at which the increase in fuel supply amount due to startup fuel amount increase control is reduced when the engine operating condition satisfies a predetermined condition, even before the startup fuel amount increase control is finished. This system allows immediate start of F/B control and a smooth shift from open control to F/B control.
In the double sensor systems described above, both the main F/B control and the sub-F/B control employ PID control or PI control. In the PID control and the PI control, the value of a proportional and the value of an integral (and the value of a differential in the case of the PID control) are calculated based on the deviation between an output value of the air-fuel ratio sensor and the target air-fuel ratio, the obtained values of the proportional and integral are summed up to calculate a correction amount, and the fuel supply amount and an output value of the upstream air-fuel ratio sensor are corrected based on the obtained correction amount.
The value of the integral is proportional to the integral of the deviation between the output value of the air-fuel ratio sensor and the target air-fuel ratio from the start of the F/B control. Here, the deviation between the output value of the air-fuel ratio sensor and the target air-fuel ratio is large because of the increase in fuel amount during the startup fuel amount increase control. Thus, if the F/B control is started before the startup fuel amount increase control is finished, the value of the integral is calculated based on the large deviation, which causes the value of the integral after the startup fuel amount increase control is finished to greatly deviate from an appropriate value.